Dynamic mechanical properties of plasticized polyvinyl acetate

DYNAMIC MECHANICAL PROPERTIES OF PLASTICIZED POLYVINYL ACETATE 1 Malcolm L. Williams 2 and John D. Ferry

Department of Chemistry, University of Wisconsin, Madison, Wisconsin Received October 18, 195~ INTRODUCTION

Although numerous studies of the dynamic mechanical properties of concentrated polymer solutions have been described, very few have extended to high enough frequencies or low enough temperatures to encompass the transition (as a function of frequency) from soft and rubberlike to glasslike consistency (1). Such measurements are reported here for a 50% solution (by volume) of polyvinyl acetate in tri-m-cresyl phosphate. The same polymer sample has been extensively studied in the undiluted state (2), as well as in solution under conditions corresponding to the plateau and terminal regions of the relaxation spectrum (3-5). To correlate the latter with the new measurements in the transition region, the steady-flow viscosity of the 50 % solution in tri-m-cresyl phosphate has also been determined. MATERIALS AND METHODS

The polyvinyl acetate was an unfractionated sample of grade AYAX, lot 1232, furnished through the kindness of Mr. A. K. Doolittle of Carbide and Carbon Chemicals Company. Its properties have been described in the preceding paper (2) and elsewhere (3-5). The tri-m-cresyl phosphate was practical grade, from the Eastman Kodak Company. The solution (50 % by volume, calculated 50.5 % by weight) was mixed in an arrangement designed by Mr. D. J. Plazek; a flask containing a Teflon-covered piece of magnetized iron imbedded in the mixture was very slowly rotated between the poles of a powerful magnet, while warmed to approximately 60°C. by an infrared lamp. Steady-flow viscosities were measured by the falling-cylinder apparatus of Fox and Flory (6) as modified in this laboratory (7). Measurements of 1 P a r t X V I I of a series on Mechanical Properties of Substances of High Molecular Weight. 2 Union Carbide and Carbon Fellow in Physical Chemistry, 1952-1954. 1

2

M. L. WILLIAMS AND J. D. FERRY TABLE I

Steady-Flow Viscosities Temp., °C. --0 5 7 17 25 34 41

Log 10.14 9.41 8.39 7.77 7.02 6.49

the complex shear compliance (J* = J ' - i J " ) were made with the double transducer of Fitzgerald and Ferry (8), as modified by Fitzgerald (9). STEADY-FLOW VISCOSITIES

Logarithms of the steady-flow viscosity at six temperatures are given in Table I. These values, plotted against 1 / T 2, where T is the absolute temperature, gave a straight line, thus conforming to the relationship previously found empirically for undiluted polyisobutylene (6); the slope was 1.1 × 10e deg?, about twice that for polyisobutylene (6, 9). The viscosity of the solvent at 25°C. was 0.57 poiseS; thus the logarithm of the relative viscosity of the polymer solution at this temperature was 8.02. This fits in reasonably with values at lower concentrations in different solvents (10), on the basis that the relative viscosity is approximately a function of volume concentration alone. DYNAMIC MEASUREMENTS

For the transducer measurements, three pairs of disc-shaped samples were employed. Samples 42 had dimensions of 1 ~ 6 in. (diameter) by ~ 2 in. (thickness) and, after compression, a sample coefficient (8) of 67.5 em. at 25°C. Samples 40, 1~6 in. by ~ 2 in., had a nominal coefficient of 20.1, and samples 41, 11/~2 in. by 3~6 in., a nominal coefficient of 3.19, both at 25°C. Check runs following any temperature sequence below 30°C. agreed well with initial measurements; but after samples 42 had been taken to higher temperatures, check runs at 25°C. gave values of J ' and J " about 10 % lower than the original. Since the J " / J ' ratios were unchanged, this deviation was attributed to sag, and the data reported for 35.1°C. and 40.0°C. may therefore be somewhat less precise than at the other temperatures. The nominal sample coefficients for 40 and 41 were adjusted by empirical corrections of -t-11% and - 7 . 7 % , respectively, to bring the values of J ' and J " into coincidence with those for samples 42; in the former case the deviation was attributed to sag during mounting of the samples, and in the latter to bulging. 3 We are indebted to Mr. Donald M. Stern for this value.

PROPERTIES

OF PLASTICIZED i

~

POLYVINYL

r

i

r

ACETATE

i

3

J

~4e

•

~

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FRE OUENC Y - CPS- (L OGARI THMICI

FIG. 1. Variation of the real part of the dynamic shear compliance, J', with frequency for polyvinyl acetate plasticized by tri-m-cresyl phosphate (50% by volume) at eleven temperatures as indicated. Sample coefficients at temperatures other than 25°C. were calculated, as usual, on the assumption that the sample thickness remained constant. The thermal expansion was calculated from measurements of density (p), which could be approximated by the equation p = 1.183 - 0.86 X 10-3 (t - 25), where t is Centigrade temperature. Values of J ' and J " at eleven temperatures from - 1 1 ° C . to 40°C. are shown as double logarithmic plots against frequency (from 30 to 4500 cycles per second) in Figs. 1 and 2. Where data on different samples were taken at the same frequencies and temperatures, the values have been averaged. Complete numerical data are recorded elsewhere (11). Over this range of temperatures and frequencies, J ' varies from 10 -6.0 to 10 -g.6, and J~' from 10-e-3 to 10-~°.°. For application of the method of reduced variables, the usual double logarithmic plots of J'p and J"p were prepared (2, 9), using 298°K. as the reference temperature, with J® estimated as 1.5 X 10-l° cm?/dyne. Values of log at, the reduction factor expressing the change of all retardation times with temperature, obtained from J'p and J"p were in good agreement; they are listed in Table II. Values of J'p and J"p plotted against (oat (where ~ is the circular fre-

4

M.L.

WILLIAMS AND J. D. FERRY

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FIG. 2. Variation of the imaginary part of the dynamic shear compliance, J% with frequency for polyvinyl acetate plasticized by tri-m-cresyl phosphate at eleven temperatures as indicated. TABLE II Reduction Factors Temp., °C.

Log a T

Temp., *C.

Log a T

--10.8 --5.8

4.54 3.57

20.0 25.0 29.9 35.1 40.0

0.42 0.00 --0.35

--0.9

2.80

4.4 9.5 14.8

2.10 1.48 0.93

--0.65

--0.90

quency), with double logarithmic scales, are shown in Figs. 3 and 4. D a t a at all temperatures and frequencies superpose to give composite curves representing j t and J " at 25°C. from 101.4 to 109-1 sec. -1. From these curves, G' and G 'p, the components of the complex rigidity, and y', the real part of the complex viscosity, have been calculated; they are shown in Fig. 5, again using double logarithmic scales, at the standard temperature of 25°C. The shapes of all these curves are rather similar to those previously given for the undiluted polymer (2). However, the loss tangent J " / J ' = G " / G ' ,

PROPERTIES OF PLASTICIZED POLYVINYL ACETATE

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-7

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FIo. 3. Real part of the eomplex compiianee reduced to 25°C., plotted logarithmically against reduced frequency. Temperature key same as in Figs. 1 and 2.

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FIG. 4. I m a g i n a r y p a r t of t h e complex compliance reduced to 25°C., p l o t t e d logar i t h m i c a l l y against reduced frequency. T e m p e r a t u r e key same as in Figs. 1 and 2.

in which small differences are more obvious, shows a somewhat broader and lower maximum in the plasticized polymer; a similar and more marked broadening by diluent is shown also in comparing polystyrene with a 62 % solution of the latter in decalin (Fig. 6).

6

M . L . WILLIAMS AND,J. D. FERRY

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FIG. 5. Real and imaginary parts of the complex shear modulus, G' and Gn, and the real part of the complex viscosity, ~', reduced to 25°C., plotted logarithmically against reduced frequency.

~:

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I

I

i

I

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I 5

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FIG. 6. Loss tangents (J~'/J' = G~'/G'), plotted logarithmically against reduced frequency for (1) polyvinyl acetate, reduced to 75°C., (2) 50% (by volume) solution of polyvinyl acetate in tri-m-cresyl phosphate, reduced to 25°C., (3) polystyrene, reduced to 125°C., and (4) 62% solution (by weight) of polystyrene in decalin, reduced to 25°C.

PROPERTIES OF PLASTICIZED POLYVINYL ACETATE TABLE

7"

III

Relaxation and Retardation Distribution Functions Reduced to ~5°C. Log ~l,p (dyne/cm.~) Log rp (sec.) --9.0 --8.5 --8.0 --7.5 --7.0 --6.5 --6.0 --5.5 --5.0 --4.5 --4.0 --3.5 --3.0 --2.5 --2.0 --1.5

From G' 8.61 8.74 8.80 8.80 8.81 8.60 8.32 7.96 7.43 6.84 6.45 6.17 5.91 5.69 5.42 5.20

From Gn 8.94 8.93 8.91 8.89 8.78 8.65 8.44 8.06 7.50 7.05 6.64 6.26 5.97 5.67 5.46 5.27

Log Lp (cm.~/dyne) From ] ' ---10.45 --10.33 --10.17 --9.94 --9.70 --9.46 --9.26 --8.89 --8.39 --7.91 --7.38 --6.97 --6.67 --6.53 --6.55

From jn --10.31 --10.28 --10.15 --9.98 --9.80 --9.59 --9.37 --9.10 --8.78 --8.45 --7.87 --7.41 --7.01 --6.74 --6.52 --6.52

DISTRIBUTION FUNCTIONS

The relaxation and retardation distribution functions, Cp and L~, reduced to 25°C., have been calculated in the usual manner from our second approximation formulas (12), and values are listed in Table III. The values from the real and imaginary components of the measurements are in good agreement in both cases. The relaxation distribution was also obtained from G' and G" by the method of Schwarzl and Staverraan (13); the results were very similar, as previously found in a comparison of the two methods of calculation for the undiluted polyvinyl acetate (2). The distribution functions resemble in shape those for the undiluted polymer (2); in particular, near • = 106 both relaxation spectra have the theoretical slope of _1/~ on a double logarithmic scale, specified by a modification (14) of the Rouse theory (15): = (1/2~¢/6)(apN0/M0)(~0kT)½r -~ where a = (-~o2Mo/M) ½, ~o~ is the mean square end-to-end separation of the polymer molecule, M0 and M the molecular weights of monomer unit and polymer, respectively, p the density, No Avogadro's number, ~0 the monomeric friction coefficient, and k Boltzmann's constant. For a solution, p is replaced by c, the concentration in g./ml. The effect of plasticization on the friction coefficient can thus be calculated, if the spectra for both undiluted and plasticized systems are reduced to a common temperature. For the undiluted polymer, the mechanical measurements do not ex-

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WILLIAMS AND J, D, FERRY

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L~ r, FIG. 7. Distribution function of mechanical relaxation times (¢r) reduced to unit density and unit steady-flow viscosity at 25°C. Solid curve: left of short dashes, polyvinyl acetate in tri-m-cresyl phosphate; right of short dashes, polyvinyl acetate in trichloropropane. Dashed curve: polystyrene in decalin. Short dashes indicate no experimental measurements in this region. tend below 50°C., but the electrical reduction factor br is available at lower temperatures, permitting comparison of the two systems at 40°C.; the identity of ar and br at higher temperatures (2) justifies this procedure. From the data of the preceding paper (2), A log ar for the interval from 75°C. to 40°C. for the undiluted polymer is 4.85, whereas from Table II for the 50% solution it is - 0 . 9 0 for the interval from 25°C. to 40°C. The value of a should be close to that of the polymer in a e-solvent (16), which from the data of Shultz (17) is estimated to be 2.8 A. for polyvinyl acetate. B y interpolating values of r for ~/p and ¢ / c = 10 ~, we find log i'0 (in dyne sec./cm.) at 40°C. to be 2.53 for the undiluted polymer and - 4 . 4 7 for the 50 % solution. Thus the introduction of the diluent diminishes the monomeric friction coefficient b y a factor of about 107. T o correlate the transition zone of the relaxation spectrum in Table I I I with the plateau and terminal zones previously studied in concentrated solutions (in 1,2,3-trichloropropane), the former must be reduced to a reference state of unit viscosity and concentration, using the relations • ~ = ~ p / c and r~ = ~pc/~, where ~ is the steady-flow viscosity at 25°C. The function thus reduced is plotted in Fig. 7; it fits in quite well with the plateau (3, 4) and terminal (5) zones, which are also shown. The

PROPERTIES OF PLASTICIZED POLYVINYL ACETATE

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I 0 40

Temperoture, °C FIG. 8. Logarithm of reduction factor aT and apparent energy of activation &H, plotted against temperature. Key to points : open circles, log aT from dynamic measurements; solid circles, log aT from steady-flow viscosity; crossed circles, AH~.

minimum numerical slope of the log-log plot in the plateau region is 0.15; as in solutions of other vinyl polymers of similar molecular weight, the plateau is not horizontal. The whole composite function is very similar to that previously found for concentrated polystyrene solutions (1), shown as a dashed curve. These two polymer samples are of closely similar weightaverage molecular weight (polyvinyl acetate 420,000, polystyrene 370,000) and are fairly similar in number-average (140,000 and 197,000, respectively); the close coincidence of their relaxation spectra when reduced to standard reference states is further support for the view that the mechanical behavior of such polymers depends almost entirely on the backbone structure and not on the nature of the side chains. TEMPERATURE DEPENDENCE OF MECHANICAL PROPERTIES

According to the method of reduced variables, the reduction factor ar should be obtainable not only from empirical shifts of the dynamic data but also from the temperature dependence of ~;ar = ~Toco/~oTc, where and c refer to the temperature of measurement and 70 and Coto the reference temperature (here 25°C.). Values of ar from both sources are plotted in Fig. 8; they agree quite well, although those from viscosity change somewhat less rapidly with temperature. The apparent activation energy for relaxation processes, AHa = R d l n a r / d ( 1 / T ) , is also plotted in Fig. 8, and shows the usual rapid increase with decreasing temperature. Interrelation of such curves for different polymer systems will be discussed in a future communication.

~t0

M . L . WILLIAMS AND J. D. FERRY ACKNOWLEDGMENTS

This work was part of a program of research on the physical structure and properties of cellulose derivatives and other polymers supported by the Allegany Ballistics Laboratory, Cumberland, Maryland, an establishment owned by the United States Navy and operated by the Hercules Powder Company under Contract NOrd 10431. It was also supported in part by a grant from Research Corporation and by the Research Committee of the Graduate School of the University of Wisconsin from funds supplied by the Wisconsin Alumni Research Foundation. The fellowship in Physical Chemistry given by Union Carbide and Carbon Corporation is gratefully acknowledged. We are much indebted to Mrs. J. C. Alexander for assistance in calculations. SUMMARY

The real and imaginary components of the complex compliance have been measured between 30 and 4500 cycles per second in the temperature range -11°C. to 40°C. for a 50 % (by volume) solution of polyvinyl acetate in tri-m-cresyl phosphate. Results at all temperatures and frequencies superpose by the method of reduced variables to give the components at 25°C. over 7.5 decades of frequency, corresponding to the transition from rubberlike to glasslike consistency at this temperature. Values of the steady-flow viscosity have been measured between 0 ° and 41°C. and found to give nearly the same temperature reduction factors as found empirically from the dynamic measurements. Relaxation and retardation distribution functions have been calculated, By reducing these da~a to a common temperature for both plasticized and undiluted polymer, it is concluded that the presence of 50 % diluent reduces the monomeric friction coefficient by a factor of 107.IBy reducing the data to a hypothetical reference state of unit density and unit steady-flow viscosity and combining them with previous data on solutions of the same polymer in 1,2,3-trichloropropane, the distribution function of mechanical relaxation times can be obtained at 25°C. over 13.5 decades of time. The distribution function is found to be similar in shape and location on the time scale to that obtained for polystyrene in decalin previously studied in this laboratory. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.

GRANDINE,L. D., JR., AND FERRY, J. D., J. Appl. Phys. 24, 679 (1953). WILLIAMS,M. L., AND FERRY, J. D., J. Colloid Sc/: 9, 479 (1954). SAWYER,W. M., AND FERRY, J. D., J . A m . Chem. Soc. 72, 5030 (1950). FERRY, J. D., SAWYER,W. M., BROWNING, G. V., AND GROTH, A. H., JR., J. Appl. Phys. 21,513 (1950). FERRY,J. D., WILLIAMS,M. L., ANDSTERN, D.M., J. Phys. Chem. 55, 987 (1954). Fox, T. G., AND FLORY, P. J., J. Am. Chem. Soc. 70, 2384 (1948). FERRY, J. D., GRANDINE,L. D., JR., AND UDY, D. C., J. Colloid Sci. 8, 529 (1953). FITZGERALD,E. R., AND FERRY, J. D., J. Colloid Sci. 8, 1 (1953). FERRY, J. D., GRANDINE, L. D., JR., AND FITZGERALD, E. R., J. Appl. Phys. 24,911 (1953).

PROPERTIES OF PLASTICIZED POLYVINYL ACETATE

11

10. FERRY, J. D., FOSTER, E. L., BROWNING, G. V., AND SAWYER,W. M., J. Colloid Sci. 6, 377 (1951). 11. WILLIAMS,M. L., Ph.D. Thesis, University of Wisconsin, Madison, 1954. 12. WILLIAMS,1~. L., AND FERRY, J. D., J. Polymer Sci. 11,169 (1953). 13. SCHWARZL,F., AND STAVERMAN,A. J., Appl. Sci. Research A4, 127 (1953). 14. FERRY, J. D., LANDEL, R. F., AND WXLLIAMS,M. L., J. Appl. Phys. (in press). 15. ROUSE, P. E., JR., J. Chem. Phys. 21, 1272 (1953). 16. FLORY, P. J., J. Chem. Phys. 17, 303 (1949). 17. S~ULTZ, A. R., J. Am. Chem. ~oc. 78, 3422 (1954).